However, after working out the math, it appears that the optimal strategy against this one is actually a very nice one.
Of course, the same as in a game of chicken where your opponent precommits to defecting.
In infinite IPD:
There are lots of probabilistic strategies your opponent can precommit to that prevent you from averaging CC (in this case: 3).
If your opponent accepts any probabilistic precommitment from you without precommiting himself, you can maximise your score beyond CC.
If you model your opponent as a probabilistic strategy, you accept any probabilistic precommitment from your opponent.
Point 2 may not be obvious, but follows straight from the payoff matrix.
Well, yes; I’m assuming that I know the strategy my opponent is playing, which assumes a precommitment. I’m just trying to explain the reasoning in the paper, without going into determinants and Markov chains and so on.
Of course, the same as in a game of chicken where your opponent precommits to defecting.
In infinite IPD:
There are lots of probabilistic strategies your opponent can precommit to that prevent you from averaging CC (in this case: 3).
If your opponent accepts any probabilistic precommitment from you without precommiting himself, you can maximise your score beyond CC.
If you model your opponent as a probabilistic strategy, you accept any probabilistic precommitment from your opponent.
Point 2 may not be obvious, but follows straight from the payoff matrix.
Well, yes; I’m assuming that I know the strategy my opponent is playing, which assumes a precommitment. I’m just trying to explain the reasoning in the paper, without going into determinants and Markov chains and so on.